Title
Weyl number methods for the investigation of spectral
asymptotics of matrix and integral operators

AbstractWe give an overview of methods for the determination of the
asymptotic behavior of the eigenvalue sequence of bounded
linear operators in Banach spaces. Particular emphasis will
be put on estimates of eigenvalues via Weyl numbers in
contrast to the more often used entropy numbers. While
the study of the asymptotic behavior of eigenvalue sequences
is by now a classical field of research with many
applications, it is still a very active area. We demonstrate
this by deriving new results for the spectral asymptotics
of certain weakly singular integral operators on fractal
sets which complements and extends the recent study of
M. Zähle on Riesz potentials and Liouville operators
on fractal sets.